According to the parabolic equation (e.g., Pazy [1]}),
the solution guaranteed by Theorem 6.1 is called a strong solution
of the fractional partial differential equation, while the solution to
an integrated equation (6.10) is called a mild solution.
Proposition 6.1 asserts the equivalence between these two kinds of
solutions under assumption that \(a\in H^1_0(\Omega )\)  and
\(F \in L^2(0,T;L^2(\Omega ))\) .
